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Maullin-Sapey T, Schwartzman A, Nichols TE. Spatial confidence regions for combinations of excursion sets in image analysis. J R Stat Soc Series B Stat Methodol 2024; 86:177-193. [PMID: 38344135 PMCID: PMC10852994 DOI: 10.1093/jrsssb/qkad104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2022] [Revised: 04/03/2023] [Accepted: 07/27/2023] [Indexed: 06/02/2024]
Abstract
The analysis of excursion sets in imaging data is essential to a wide range of scientific disciplines such as neuroimaging, climatology, and cosmology. Despite growing literature, there is little published concerning the comparison of processes that have been sampled across the same spatial region but which reflect different study conditions. Given a set of asymptotically Gaussian random fields, each corresponding to a sample acquired for a different study condition, this work aims to provide confidence statements about the intersection, or union, of the excursion sets across all fields. Such spatial regions are of natural interest as they directly correspond to the questions 'Where do all random fields exceed a predetermined threshold?', or 'Where does at least one random field exceed a predetermined threshold?'. To assess the degree of spatial variability present, our method provides, with a desired confidence, subsets and supersets of spatial regions defined by logical conjunctions (i.e. set intersections) or disjunctions (i.e. set unions), without any assumption on the dependence between the different fields. The method is verified by extensive simulations and demonstrated using task-fMRI data to identify brain regions with activation common to four variants of a working memory task.
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Affiliation(s)
- Thomas Maullin-Sapey
- Nuffield Department of Population Health, Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, University of Oxford, Oxford, UK
| | - Armin Schwartzman
- Division of Biostatistics, University of California, San Diego, CA, USA
- Halicioğlu Data Science Institute, University of California, San Diego, CA, USA
| | - Thomas E Nichols
- Nuffield Department of Population Health, Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, University of Oxford, Oxford, UK
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2
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Director HM, Raftery AE. Contour models for physical boundaries enclosing star‐shaped and approximately star‐shaped polygons. J R Stat Soc Ser C Appl Stat 2022. [DOI: 10.1111/rssc.12592] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hannah M. Director
- Department of Statistics University of Washington Seattle Washington USA
| | - Adrian E. Raftery
- Departments of Statistics and Sociology University of Washington Seattle Washington USA
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3
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Hazra A, Huser R. Estimating high-resolution Red Sea surface temperature hotspots, using a low-rank semiparametric spatial model. Ann Appl Stat 2021. [DOI: 10.1214/20-aoas1418] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Arnab Hazra
- Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, King Abdullah University of Science and Technology (KAUST)
| | - Raphaël Huser
- Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, King Abdullah University of Science and Technology (KAUST)
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4
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Fossum TO, Travelletti C, Eidsvik J, Ginsbourger D, Rajan K. Learning excursion sets of vector-valued Gaussian random fields for autonomous ocean sampling. Ann Appl Stat 2021. [DOI: 10.1214/21-aoas1451] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Trygve Olav Fossum
- Department of Marine Technology, Norwegian University of Science and Technology (NTNU)
| | - Cédric Travelletti
- Institute of Mathematical Statistics and Actuarial Science, University of Bern
| | - Jo Eidsvik
- Department of Mathematical Sciences, NTNU
| | - David Ginsbourger
- Institute of Mathematical Statistics and Actuarial Science, University of Bern
| | - Kanna Rajan
- Underwater Systems and Technology Laboratory, Faculty of Engineering, University of Porto
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5
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Moser GE, Ghosh S. Finding exceedance locations in a large spatial database using nonparametric regression. ECOLOGICAL COMPLEXITY 2021. [DOI: 10.1016/j.ecocom.2020.100905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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6
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Azzimonti D, Ginsbourger D, Chevalier C, Bect J, Richet Y. Adaptive Design of Experiments for Conservative Estimation of Excursion Sets. Technometrics 2019. [DOI: 10.1080/00401706.2019.1693427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Dario Azzimonti
- Istituto Dalle Molle di studi sull’Intelligenza Artificiale (IDSIA), Scuola universitaria professionale della Svizzera italiana (SUPSI), Università della Svizzera italiana (USI), Manno, Switzerland
| | - David Ginsbourger
- Uncertainty Quantification and Optimal Design Group, Idiap Research Institute, Martigny, Switzerland
- IMSV, Department of Mathematics and Statistics, University of Bern, Bern, Switzerland
| | - Clément Chevalier
- Institute of Statistics, University of Neuchâtel, Neuchâtel, Switzerland
| | - Julien Bect
- Laboratoire des Signaux et Systèmes (UMR CNRS 8506), CentraleSupelec, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Gif-sur-Yvette, France
| | - Yann Richet
- Institut de Radioprotection et de Sûreté Nucléaire (IRSN), Paris, France
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Xu P, Lee Y, Shi JQ, Eyre J. Automatic detection of significant areas for functional data with directional error control. Stat Med 2019; 38:376-397. [PMID: 30225994 DOI: 10.1002/sim.7968] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2017] [Revised: 07/30/2018] [Accepted: 08/22/2018] [Indexed: 11/11/2022]
Abstract
In this paper, we propose a large-scale multiple testing procedure to find the significant sub-areas between two samples of curves automatically. The procedure is optimal in that it controls the directional false discovery rate at any specified level on a continuum asymptotically. By introducing a nonparametric Gaussian process regression model for the two-sided multiple test, the procedure is computationally inexpensive. It can cope with problems with multidimensional covariates and accommodate different sampling designs across the samples. We further propose the significant curve/surface, giving an insight on dynamic significant differences between two curves. Simulation studies demonstrate that the proposed procedure enjoys superior performance with strong power and good directional error control. The procedure is also illustrated with the application to two executive function studies in hemiplegia.
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Affiliation(s)
- Peirong Xu
- College of Mathematics and Sciences, Shanghai Normal University, Shanghai, China
| | - Youngjo Lee
- Department of Statistics, Seoul National University, Seoul, Korea
| | - Jian Qing Shi
- School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, UK
| | - Janet Eyre
- Institute of Neuroscience, Newcastle University, Newcastle upon Tyne, UK
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8
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Azzimonti D, Ginsbourger D. Estimating Orthant Probabilities of High-Dimensional Gaussian Vectors with An Application to Set Estimation. J Comput Graph Stat 2018. [DOI: 10.1080/10618600.2017.1360781] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Dario Azzimonti
- UQOD Group, Idiap Research Institute, Martigny, Switzerland
- IMSV, Department of Mathematics and Statistics, University of Bern, Bern, Switzerland
| | - David Ginsbourger
- UQOD Group, Idiap Research Institute, Martigny, Switzerland
- IMSV, Department of Mathematics and Statistics, University of Bern, Bern, Switzerland
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9
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Sommerfeld M, Sain S, Schwartzman A. Confidence regions for spatial excursion sets from repeated random field observations, with an application to climate. J Am Stat Assoc 2018; 113:1327-1340. [PMID: 31452557 PMCID: PMC6709714 DOI: 10.1080/01621459.2017.1341838] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2015] [Revised: 04/27/2017] [Indexed: 10/19/2022]
Abstract
The goal of this paper is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations. Given an asymptotically Gaussian estimator of the target function, a pair of data-dependent nested excursion sets are constructed that are sub- and super-sets of the true excursion set, respectively, with a desired confidence. Asymptotic coverage probabilities are determined via a multiplier bootstrap method, not requiring Gaussianity of the original data nor stationarity or smoothness of the limiting Gaussian field. The method is used to determine regions in North America where the mean summer and winter temperatures are expected to increase by mid 21st century by more than 2 degrees Celsius.
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French JP, McGinnis S, Schwartzman A. Assessing NARCCAP climate model effects using spatial confidence regions. ADVANCES IN STATISTICAL CLIMATOLOGY, METEOROLOGY AND OCEANOGRAPHY 2017; 3:67-92. [PMID: 28936474 PMCID: PMC5604436 DOI: 10.5194/ascmo-3-67-2017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We assess similarities and differences between model effects for the North American Regional Climate Change Assessment Program (NARCCAP) climate models using varying classes of linear regression models. Specifically, we consider how the average temperature effect differs for the various global and regional climate model combinations, including assessment of possible interaction between the effects of global and regional climate models. We use both pointwise and simultaneous inference procedures to identify regions where global and regional climate model effects differ. We also show conclusively that results from pointwise inference are misleading, and that accounting for multiple comparisons is important for making proper inference.
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Affiliation(s)
- Joshua P. French
- Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO 80204, USA
| | - Seth McGinnis
- Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, Boulder, CO 80307, USA
| | - Armin Schwartzman
- Division of Biostatistics, University of California, San Diego, La Jolla, CA 92093, USA
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Yan Y, Wang H, Shen X, Zhong X. Decision Fusion with Channel Errors in Distributed Decode-Then-Fuse Sensor Networks. SENSORS 2015; 15:19157-80. [PMID: 26251908 PMCID: PMC4570364 DOI: 10.3390/s150819157] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/13/2015] [Revised: 07/19/2015] [Accepted: 07/30/2015] [Indexed: 11/25/2022]
Abstract
Decision fusion for distributed detection in sensor networks under non-ideal channels is investigated in this paper. Usually, the local decisions are transmitted to the fusion center (FC) and decoded, and a fusion rule is then applied to achieve a global decision. We propose an optimal likelihood ratio test (LRT)-based fusion rule to take the uncertainty of the decoded binary data due to modulation, reception mode and communication channel into account. The average bit error rate (BER) is employed to characterize such an uncertainty. Further, the detection performance is analyzed under both non-identical and identical local detection performance indices. In addition, the performance of the proposed method is compared with the existing optimal and suboptimal LRT fusion rules. The results show that the proposed fusion rule is more robust compared to these existing ones.
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Affiliation(s)
- Yongsheng Yan
- School of Marine Science and Technology, Northwestern Polytechnical University,127 Youyi West Road, Xi\'an 710072, China.
| | - Haiyan Wang
- School of Marine Science and Technology, Northwestern Polytechnical University,127 Youyi West Road, Xi\'an 710072, China.
| | - Xiaohong Shen
- School of Marine Science and Technology, Northwestern Polytechnical University,127 Youyi West Road, Xi\'an 710072, China.
| | - Xionghu Zhong
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore.
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12
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Bolin D, Lindgren F. Excursion and contour uncertainty regions for latent Gaussian models. J R Stat Soc Series B Stat Methodol 2014. [DOI: 10.1111/rssb.12055] [Citation(s) in RCA: 70] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- David Bolin
- Chalmers University of Technology, Gothenburg; Sweden
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